Þórsmörk (Thorsmork) is one of the most popular hiking areas in Iceland, 63 km from Guesthouse Nonni.
A part of the road is graveled and you have to cross rivers (no bridges). A 4x4 is a must!
How to get there: If you do not want to drive by your rented car you can go by bus (goes dayly from Hella. Bus stop 400 m from the guesthouse). It is also possible to hire a "Super Jeep" with a driver guide.
On your way to Þórsmörk you would probably stop by the beautiful waterfall Seljalandsfoss (you can walk behind it), Gljúfrabúi is also a waterfall in a little ravine only few hundred meters away from Seljalandsfoss.
A trip to Þórsmörk is a good daytour.
See further information in Wikipedia.